We want to describe each one of the given functions as translations of a parent function.
The descriptions are:
1) This is a translation of 4 units to the left.
2) This is a translation of 4 units to the right.
3) This is a vertical translation of 2 units down.
4) This is a vertical translation of 2 units up.
First, we need to describe translations.
Horizontal translation.
For a given function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
Where if N is positive the translation is to the left, if N is negative the translation is to the right.
Vertical translation.
For a given function f(x) a vertical translation is written as:
g(x) = f(x) + N
Where if N is positive the translation is upwards, and if N is negative the translation is downwards.
Now we have the parent function:
f(x) = √x
Then each one of the transformations can be described by knowing how the translations work:
1) y = √(x + 4) = f(x + 4)
This is a translation of 4 units to the left.
2) y = √(x - 4) = f(x - 4)
This is a translation of 4 units to the right.
3) y = √x - 2 = f(x) - 2
This is a vertical translation of 2 units down.
4) y =√x + 2 = f(x) + 2
This is a vertical translation of 2 units up.
If you want to learn more, you can read:
https://brainly.com/question/24401156
